Step-by-step explanation:
using gp formula
tn=ar^n-1
which our a which is the first term is = -3
our r which is t2/t1=-6
t8=(-3)(-6)^8-1
=(-3)(-6)^7
=(-3)(-279936)
=839808
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
-f(*) = (x + 2)(x - 6)
f(x) = (x - 4)(x + 3)
f(x) = (x - 12)(x 1)
f(x) = (x -3)(x + 4)
The standard form of the given quadratic equation in factored form is
(x+2) (x-6) = x²-4x-12
(x-4) (x+3) = x²-x-12
(x-12) (X+1) = x²-11x-12
(x-3) (x+4) = x²+x-12
what are quadratic equations?
A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero
To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.
f(x) = (x+2) (x-6)
x²+2x-6x-12
x²-4x-12
similarly, the standard form of equations 2,3 and 4 are :
(x²-x-12)
(x²-11x-12)
(x²+x-12)
Learn more about quadratic function here:
brainly.com/question/4119784
#SPJ1
Answer:
B, D, A, C
Step-by-step explanation:
f(x) = (x + 2)(x – 6)
✔ B
f(x) = (x – 4)(x + 3)
✔ D
f(x) = (x – 12)(x + 1)
✔ A
f(x) = (x – 3)(x + 4)
✔ C
Help please !!!!!!! Need helppppp
Answer:
option c
Step-by-step explanation:
option c is a correct answer
Find the value of x in the given figure
Answer:
X=36
Step-by-step explanation:
2x + 3x=5x
if given figure is 180 then
5x=180
X=180/5
X=36
How many diagonals does a regualt hexagon have?
Answer: 9 diagonals
Step-by-step explanation:
At a sale this week, a desk is being sold for $336. This is a 36% discount from the original price.
What is the original price?
Answer:
$525
Step-by-step explanation:
We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:
[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]
To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:
525 * 0.36 = 189
525 - 189 = 336
Modeling the first formula gives us:
525 - (0.36 * 525) = 336
525 - 189 = 336
In the diagram below, if < ACD = 48 °, find the measure of < ABD.
Answer:
d
Step-by-step explanation:
the opposite angles of a cyclic quadrilateral sum to 180° , that is
∠ ABD + ∠ ACD = 180°
∠ ABD + 48° = 180° ( subtract 48° from both sides )
∠ ABD = 132°
The long division below shows the first term of the quotient. which polynomial should be subtracted from the dividend first? x 2 startlongdivisionsymbol x cubed 3 x squared x endlongdivisionsymbol to get a quotient of x squared
The polynomial that should be subtracted from the dividend first is; x³ + 2x²
How to carry out polynomial long division?
The long division we are given is;
__________
x + 2 ) x³ + 3x² + x
Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².
Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;
(x + 2) * (x²) = x³ + 2x²
Thus, the polynomial to be subtracted is x³ + 2x²
Read more about Polynomial Long division at; https://brainly.com/question/28032495
#SPJ1
Gustavo is in a contest where he will win one of four possible prizes. he creates a four-part spinner to represent the four prizes that he has an equal chance of winning: a video game system, a bicycle, a watch, and a gift card. he spins the spinner several times to demonstrate the likelihood of winning a certain prize. what is true about gustavo’s method of data collection and his data on the possible prizes?
Answer:
Gustavo used a simulation where the data is quantitative’
Please help with number 5 I tried it but I’m very confused :(
Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]
Step-by-step explanation:
Given information
Number of coins = 24 coins
Total amount = $1.95
Dime = 10 cents = $0.1
Nickel = 5 cents = $0.05
Set variables
Let d be the number of dimes
Let n be the number of nickels
Set a system of equation
1) d + n = 24
2) 0.1d + 0.05n = 1.95
Multiply 10 on both sides of 2) equation
0.1d · 10 + 0.05n · 10 = 1.95 · 10
d + 0.5n = 19.5
Current system
1) d + n = 24
2) d + 0.5n = 19.5
Subtract 2) equation from the 1) equation
(d + n) - (d + 0.5n) = (24) - (19.5)
Expand the parenthesis
d + n - d - 0.5n = 24 - 19.5
Combine like terms
d - d + n - 0.5n = 4.5
0.5n = 4.5
Divide 0.5 on both sides
0.5n / 0.5 = 4.5 / 0.5
[tex]\Large\boxed{n=9}[/tex]
Substitute the n value into one of the equations to find the d value
d + n = 24
d + (9) = 24
d = 24 - 9
[tex]\Large\boxed{d=15}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A large container holds 4 gallons of chocolate milk that has to be poured into 1-pint bottles. if the ratio of gallons to pints is 1 : 8, how many bottles are needed? a. 2 bottles b. 4 bottles c. 8 bottles d. 32 bottles e. 40 bottles
32 bottles are needed to poured 4 gallons of chocolate milk.
The correct option is D.
What do you know about volume?A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.
According to the given information:Pints to Gallons Ratio: 1:8
Permit x bottles to be present.
There are x bottles required for 4 gallons of chocolate milk.
Because of the direct proportion
4/x = 1/8
x = 4 x 8
x = 32
As a result, 32 bottles are required.
To know more about volume visit:
https://brainly.com/question/1739219
#SPJ4
P (-7, 1) T(x,y)= (x+9, y - 3) find the image of the given point under the given translation
[tex](-7+9, 1-3)=\boxed{(2, -2)}[/tex]
The answer is (2,-2).
What do we mean by translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.A transformation known as a translation involves shifting each point in a figure by the same amount and in the same direction. For instance, this transformation shifts the parallelogram 3 units upward and 5 units to the right.A transformation in geometry is an action that moves, flips, or modifies a shape (referred to as the preimage) to produce a new shape (called the image). An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction.Find the image of the given point under the given translation:
The rule of translation is (x+9, y - 3), P (-7, 1).
Here we need to add 9 from
x value is -7+9=2
y We need to subtract -3 from
y value is (1-3)=-2
So, P’=( 2,-2)
To learn more about translation, refer to:
https://brainly.com/question/24086234
#SPJ9
help pls i will give brainleast no links
Answer: 100 square cm
Step-by-step explanation: the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.
Answer: 104
Step-by-step explanation:
area of trangle =33 because 6*11/2=33
area of rectangle 9*7=63
area of rectangle 2*2=4
33+63+4=100^2
An industrial machine produces widgets, but it has a 0.12 defective rate. what is the probability that the machine produces fewer than 3 defective widgets in a production run of 75 items?
The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.
What is the probability?A probability refers to the ratio of favorable events to the n number of total events.
Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.
Given data
An industrial machine produces 3 widgets.
It has a 0.12 defective rate.
Defective rate fewer than 3
Total Probability = P of 2 defective + P for 1 defective
Total Probability = 2/74 + 1/73
Total Probability ≈ 0.04072565716
Total Probability ≈ 0.041
Therefore, the required probability for fewer than 3 defective rate is 0.041
Read more about probability
brainly.com/question/14290572
#SPJ1
Look at the equation shown below. 19 - 5 = 3 z - 11 Which of these expressions gives the value of Z
If the equation is 19-5=3z-11 then the value of z is 15/3.
Given an equation in terms of z is 19-5=3z-11.
We are required to find the value of variable z which exist in equation.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.
The value of z can be find as under:
19-5=3z-11
4=3z-11
3z=4+11
3z=15
z=15/3
Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.
Learn more about equation at https://brainly.com/question/2972832
#SPJ1
6. Solve the system of equations.
x = 3y + 1
2x+4y= 12
O (10,3)
O (4,1)
(1,4)
(3,10)
Answer:
(4, 1 )
Step-by-step explanation:
x = 3y + 1 → (1)
2x + 4y = 12 → (2)
substitute x = 3y + 1 into (2)
2(3y + 1) + 4y = 12
6y + 2 + 4y = 12
10y + 2 = 12 ( subtract 2 from both sides )
10y = 10 ( divide both sides by 10 )
y = 1
substitute y = 1 into (1)
x = 3(1) + 1 = 3 + 1 = 4
solution is (4, 1 )
Ben invests Nu 125,000 in a bank shares with a face value of Nu 100 but they are being sold at a premium of 25%. How many shares can he buy?
Answer:
This is your answer!
Step-by-step explanation:
Isabelle is mixing red paint with blue paint to make purple paint. She adds 3/10 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 1/30fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
Answer:
27/31
Step-by-step explanation:
FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31
What is the answer please
Answer:
m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131
m∠RST = 2x = 2(14) = 28
m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103
Step-by-step explanation:
m∠RSU = m∠RST + m∠TSU
10x - 9 = 2x + (2x + 75)
10x - 9 = 2x + 2x + 75
10x - 9 = 4x + 75
-4x +9 -4x +9
6x = 84
x = 14
m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131
m∠RST = 2x = 2(14) = 28
m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103
Question 1 (essay worth 4 points) (h2.02 mc) the cost of attending an amusement park is $15 for children and $40 for adults. on a particular day, the attendance at the amusement park is 5,000 attendees, and the total money earned by the park is $100,000. use the given matrix equation to solve for the number of children’s tickets sold. explain the steps that you took to solve this problem. a matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 15 and 40, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 5,000 and row 2 is 100,000.
Using a system of equations, it is found that there were 4,000 children tickets sold.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given by:
Variable x: Number of children tickets sold.Variable y: Number of adult tickets sold.The attendance at the amusement park is 5,000 attendees, hence:
x + y = 5000 -> y = 5000 - x.
Considering the cost of parking and that the total money earned by the park is $100,000, we have that:
15x + 40y = 100000
Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:
15x + 40(5000 - x) = 100000
25x = 100000
x = 100000/25
x = 4000.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
For what value of x is 3 − x equal to x − 3?
Answer:
x = 3
Step-by-step explanation:
Given the information from the question, we can deduce that:
3 - x = x - 3
Now our goal here is to find x.
3 - x = x -3
3 - x - 3 = x - 3 - 3
- x = x - 6
- x - x = x - 6 - x
- 2x = - 6
x = [tex]\frac{-6}{-2}[/tex] = 3
Answer: 3
Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.
x - 3 = 3 - x
Adding 3 to both sides, we have
x = 6 - x
Adding x to both sides we have
2x = 6
Dividing by 2 from both sides, we get
x = 3
In the circle below, if < B = 39 °, what is the measure of arc AB?
From my analysis, the answer is likely to be D. I don't have a formula to prove it though.
Answer: 78 degrees.
Step-by-step explanation:
The other guy is wrong don't listen to him.
Solve for x.
x/3 ≤ −6
x / 3 ≤ -6
---Multiply both sides by 3 to cancel out the denominator on the left side
x ≤ -18
Hope this helps!
Answer:
x=18 we multiply both 6and3please help! look at the phot linked
Answer: C
Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.
What is the product of (5 m superscript negative 2 baseline) (2 m superscript negative 3 baseline)?
Answer:
A
Step-by-step explanation:
Rearrange the equation so w is the independent variable.
u-5=-4(w-1)u−5=−4(w−1)u, minus, 5, equals, minus, 4, left parenthesis, w, minus, 1, right parenthesis
u=u=
u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1). This can be obtained by simplifying the equation and taking w to one side of the equation with other constants.
Find the rearranged equation:Simplifying an equation can be done by using the following steps:
Add/subtract the terms from the equation on both sides Multiply/divide the coefficients of the variable in order to isolate the variable Solve for the variable Substitute the variable in the original equation for finding other variables (if any)Here it is given that the equation is,
⇒ u - 5= - 4(w - 1)
We have to find an equation in which w is taken to one side of the equation with other constants.
First by adding both side of the equation with 5 we get,
⇒ u - 5 + 5 = - 4(w - 1) + 5
By opening the bracket we get,
⇒ u = - 4w + 4 + 5
Finally by adding the constants we get,
⇒ u = - 4w + 9
Hence u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1).
Learn more about algebraic equation here:
brainly.com/question/25678139
#SPJ1
The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d) find an expression for c and d in terms of a and b hence find the inverse of (2,1)
a. The expressions for c and d in terms of a and b are
c = -2b³/[(a⁴ - b⁴)a] + 1/(a - b) and d = -2b²/(a⁴ - b⁴)b. The inverse of (2,1) is (13/15, -4/15)
The question has to do with binary operation.
What is a binary operation?A binary operation is a rule of mathematical operation on two sets of elements defined on a given set.
a. How to find the expression for c and dSince The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d).
Let (e, e') be the identity element.
We know that for any binary operation * on a given set, a*e = a where e is the identity element.
So, (a,b)*(e,e') = (a,b)
So, (a,b)*(c,d) = (ac - bd, ad + bc)
(a,b)*(e,e') = (ae - be, ae' + be')
Since (a,b)*(e,e') = (a,b)
(ae - be, ae' + be') = (a, b)
So,
ae - be = a (1) and ae' + be' = b (2)e = a/(a - b) and e' = b/(a + b)
So, (e, e') = (a/(a - b), b/(a + b))
Also, for any binary operation * under a given set a*a⁻¹ = e where a⁻¹ = inverse of a.
Since (c,d) is the inverse of (a,b), we have that
(a,b)*(c,d) = (e, e')
So, (a,b)*(c,d) = (ac - bd, ad + bc)
= (a/(a - b), b/(a + b))
So,
ac - bd = a/(a - b) (3) and ad + bc = b/(a + b) (4)From (3), c = bd/a + 1/(a - b)
Substituting c into (4), we have
ad + bc = b/(a + b)
ad + b[bd/a + 1/(a - b)] = b/(a + b)
ad + b²d/a + b/(a - b) = b/(a + b)
ad + b²d/a = b/(a + b) - b/(a - b)]
(a + b²/a)d = b[1/(a + b) - 1/(a - b)]
[(a² + b²)/a]d = b[a - b - (a + b)]/(a - b)(a + b)
[(a² + b²)/a]d = b[a - b - a - b)]/(a - b)(a + b)
[(a² + b²)/a]d = b(-2b)/(a² - b²)
d = -2ab²/[(a² - b²)(a² + b²)]
d = -2ab²/(a⁴ - b⁴)
Substitutind d into c, we have
c = bd/a + 1/(a - b)
c = -2ab³/(a⁴ - b⁴)a + 1/(a - b)
c = -2b³/(a⁴ - b⁴) + 1/(a - b)
So, the expressions for c and d in terms of a and b are
c = -2b³/[(a⁴ - b⁴) + 1/(a - b) and d = -2ab²/(a⁴ - b⁴)b. What is the inverse of (2,1)Since (c,d) is the inverse of (a,b) is
c = -2b³/(a⁴ - b⁴)+ 1/(a - b) and d = -2ab²/(a⁴ - b⁴)So, with a = 2 and b = 1, c = -2b³/(a⁴ - b⁴) + 1/(a - b)
= -2(1)³/(2⁴ - 1⁴) + 1/(2 - 1)
= -2/(16 - 1) + 1/1
= -2/15 + 1
= (-2 + 15)/15
= 13/15
So, with a = 2 and b = 1, d = -2ab²/(a⁴ - b⁴)
= -2(2)(1)²/(2⁴ - 1⁴)
= -4(1)/(16 - 1)
= -4/15
So, the inverse of (2,1) is (13/15, -4/15)
Learn more about binary operation here:
https://brainly.com/question/16827196
#SPJ1
13% of a sample of 200 students do not like ice cream. what is the 95% confidence interval to describe the total percentage of students who do not like ice cream?
Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:
(8.34%, 17.66%).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the estimate and the sample size are given, respectively, by:
[tex]\pi = 0.13, n = 200[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 - 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.0834[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 + 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.1766[/tex]As a percentage, the interval is:
(8.34%, 17.66%).
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
A blimp is 1600 meters high in the air and measures the angles of depression to two stadiums to the east of the blimp. if those measurements are 71.7° and 25.2°, how far apart are the two stadiums?
The two stadiums are 2,871 meters
A blimp = point A
stadium 1 = point B
stadium 2 = point C
height of the blimp , AD = 1600
depression angle of stadium 1 , ∠y = 71.7°
depression angle of stadium 2 , ∠x = 25.2°
distance between the two stadiums = d
So, it forms 2 triangles ABD and ACD,
Using the trigonometric ratios,
tan θ = Altitude / Base
DC = AD × tan (90° - x)
= 1600 × tan( 90° - 25.2° )
= 1600 × cot(25.2°)
= 1600 × 2.13
DB = AD × tan (90° - y)
= 1600 × tan( 90° - 71.7° )
= 1600 × cot(71.7°)
= 1600 × 0.33
∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]
= 2,871 meters
To learn more about angle of depression from the given link
https://brainly.com/question/9723082
#SPJ4
What is the value of an AP: 50+45+40
Answer:
135 is correct answer of this question
y=2x + 9
3x + 2y = 4
Answer:
The answer is: (x,y) = (-2,5)
